{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:29:05Z","timestamp":1753882145865,"version":"3.41.2"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> In this paper, we introduce the notion of oriented triangular faces [Formula: see text], the notion of edges potential [Formula: see text] and the notion of triangular faces potential [Formula: see text] in a connected oriented locally finite graph [Formula: see text] in order to construct a new framework that\u2019s we call the magnetic weighted [Formula: see text]-simplicial complex [Formula: see text]. On this new magnetic weighted framework, we introduce the magnetic [Formula: see text]-cochains set, the magnetic [Formula: see text]-cochains set, the magnetic [Formula: see text]-cochains set and the magnetic cochains set. After that, we construct the magnetic [Formula: see text]-cochains Laplacian, the magnetic [Formula: see text]-cochains Laplacian, the magnetic [Formula: see text]-cochains Laplacian and the magnetic cochains Laplacian. Finally, we ensure essential self-adjointness for our new magnetic cochains Laplacians using the Stieltjes vectors. <\/jats:p>","DOI":"10.1142\/s1793830922501233","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:00:19Z","timestamp":1655456419000},"source":"Crossref","is-referenced-by-count":0,"title":["Magnetic cochains Laplacians and their essential self-adjointness"],"prefix":"10.1142","volume":"15","author":[{"given":"Azeddine","family":"Baalal","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Fondamentales et Appliqu\u00e9es, D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Sciences A\u00efn Chock, Universit\u00e9 Hassan II de Casablanca, Morocco"}]},{"given":"Khalid","family":"Hatim","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Fondamentales et Appliqu\u00e9es, D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Sciences A\u00efn Chock, Universit\u00e9 Hassan II de Casablanca, Morocco"}]}],"member":"219","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"issue":"2","key":"S1793830922501233BIB001","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s13324-014-0090-0","volume":"5","author":"Ann\u00e9 C.","year":"2015","journal-title":"Anal. 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